A Closer Look At Positive Expectation

What do I mean when I refer to an over 100% machine?” An over 100% machine simply means a machine that pays back more than you put in. Fantastic, except for one thing: this is factored over a long period of time. It does not mean over 100% in every session.” In fact, an over 100% machine isn’t guaranteed to earn you a profit even over what most would consider a long period of time. And it’s certainly not graphed by a steady upward curve. The only sure thing I’ve ever found in casino gambling is streakiness, and video poker results can be as streaky as it gets.
Also, and this is a very important concept to grasp: whether or not you achieve that over 100% return depends on the number of royals you hit. A royal contributes approximately 1.7%-2% (depending on the game) to the total payback percentage, and you only hit a royal about once every 35,000- 45,000 handssome 80 hours of play. So during those other 79 hours, even if you’re playing a deuces wild machine with a 100.76% payback percentage and accruing .5% slot club cash back for your play, that 1.8% you lose for not hitting the royal pretty much wipes out your advantage during the periods in between the big jackpot. During these periods, you will most likely lose money (positive expectation is sweet, but it usually doesn’t come easily). That’s why it’s necessary to analyze situations in terms of what mathematicians call expected value” or expected return,” which assumes an infinite period of play.
Okay, with that groundwork laid, here are a couple of examples of positive expectation readily available in any number of casinos in Las Vegas at any given time.
Playing full-pay” deuces wild with computerperfect (optimal”) strategy, the return percentage is 100.76%. Another way to say this is: for every $100
you put into a full-pay deuces wild video poker machine, you’ll get back $100.76. It may look skinny,” but that’s a pretty good edge. Unfortunately, only a computer can play computer-perfect strategy. Humans make mistakes. They get tired of sitting and staring at a screen. They get a little fuzzy from the free drinks. The guys get distracted by short skirts on cocktail waitresses. I figure skilled human strategy on a full-pay deuces wild machine is more like 100.5%. In these examples, my numbers are based on that one-half-percentage-point advantage.
Playing 25 full-pay deuces, you’re making $1.25 bets (five quarters). If you play slowly (say 320 hands per hour), you’ll put about $400 through the deuces wild machine in 60 minutes. At our skilled human capability of 100.5%, over that hour your expected return is $402 (1.005 X $400 = $402). Thus, your expected return (or win) is $2 per hour. Don’t quit your day job!
Example 2. This time you’re playing $1 deuces wild with skilled human strategy, but you’re playing fast (600 hands per hour). Betting $5 per hand, you’re putting $3,000 through the machine per hour. Now your .5% positive expected return produces $3,015; over the long term you’ll take in $15 per hour. That’s like a $30,000-a-year paycheck.

A Closer Look at Negative Expectation

The flip side of positive expectation is, logically enough, negative expectation. An under 100% machine” is a machine that pays back less than you put in. Let’s say you find a 25 deuces wild machine that has only one change in the pay table from the full- pay deuces schedule. A key changeit pays only four coins for four-of-a-kind instead of five. That’s just one tiny alteration, but it gives the house a whopping 5.7% edge. This means that you’re playing a game that returns only 94.3%. Now if you play a slow 320 hands per hour, you’re losing $22.80 per hour (.057 X $400)and that’s on a 25 machine.
Does the $2-per-hour profit from full-pay deuces look better to you now? And does the $22.80-per- hour loss convince you to read pay tables carefully? The main reason for all the new video poker variations is that casino know there are a lot of players with a little bit of video poker knowledge. Many people now know that full-pay jacks or better and deuces wild are good games, but they’re not real careful about reading the pay tables to make sure that full-pay is what they’re playing. Point them toward any jacks or better or deuces machine and they assume it pays liberally. The casinos, of course, make sure that they aren’t: Play this game. It’s almost like the other one that pays a lot more.”
This occasionally backfires on a casino when it monkeys with a pay schedule of a well-known machine and the changes result in a larger payback percentage. If you become a true student of the game, you’ll be able to spot these situations, know what changes to make in the strategy, and take advantage to make a lot of money on these machines, until the casino wises up and fixes the schedule or removes the machines entirely.

Jacks or Better

Jacks or better is the basic video poker game. One of the first to come out, it’s considered something of a video poker standard. The full-pay version is known as 9/6 jacks or better, meaning the payback (with one coin in) for a full house is 9 coins and for a flush is 6 coins. Sad to say, there are not a lot of them outside of Las Vegas. Full-pay jacks or better has a return percentage of 99.5%. It’s not a positive game; as we’ve seen, the casino has a .5% advantage. But because it’s readily available in Vegas and a lot of other video poker variations are derived from it, I also consider it the standard. Often you get enough cash back from the slot club or a promotion to make jacks or better an over 100% game.The first chart is what the pay table for a 9/6 jacks or better video poker machine looks like. The second is also a jacks or better pay table, but with a crib- cal difference: it’s an 8/5 machine. Note the difference in the payouts for full house and flush; this lowers the return to 97.3%.
As I mentioned earlier, I’m not going to provide you with the strategies, which are readily available in any number of books and computer software programs. See the Appendix for recommendations.